According to New York State Department of Taxation and Finance, a Y-203 must be filled out if you file or are required to file a New York State return, and you are a nonresident of Yonkers who earns wages or carries on a trade or business there, or are a member of a partnership that carries on a trade or business there.
For more information pertaining to this form, please click the link below:
https://www.tax.ny.gov/pdf/current_forms/it/y203i.pdf
Let me know if you have further questions.